Strength distribution of planar local load-sharing bundles

Monte Carlo simulations and probabilistic modeling are employed to understand the strength distribution of a planar bundle of local load-sharing fibers. The fibers are distributed randomly within a unit square according to a Poisson process, and the fiber strengths are Weibull distributed with exponent ρ. Monte Carlo failure simulations of bundles comprised of up to 10(5) fibers suggests that the bundle strength distribution obeys weakest-link scaling for all ρ. Also, a probabilistic model of the weakest-link event is proposed. This model introduces a failure event at a size scale between that of the fiber and that of the bundle, whose failure statistics follows that of equal load-sharing bundles. The weakest-link event is modelled as the growth of a tight cluster of these equal load-sharing bundles. The size of the equal load-sharing bundles increases with decreasing ρ. The simulated bundle strength distributions and those predicted by the model are compared, and excellent agreement is obtained.